Philbert Nang
ENS, Gabon
April 18, 2013
$D$-modules on a class of $G$-representations: We give an answer to abstract Capelli problem: Let $(G, V)$ be a multiplicity free finite dimensional representation of a connected reductive complex Lie group $G$ and $G'$ be its derived subgroup. Assume that the categorical quotient $V//G$ is one dimensional, i.e., there exists a polynomial $f$ generating the algebra of $G'$-invariant polynomials on $V ({\mathbb C} [V]^{G'} = {\mathbb C} [f])$ and such that $f \not\in \mathbb C[V]^G )$. We prove that the category of regular holonomic $D_V$-modules invariant under the action of $G$ is equivalent to the category of graded modules of finite type over a suitable algebra.
ENS, Gabon
April 18, 2013
$D$-modules on a class of $G$-representations: We give an answer to abstract Capelli problem: Let $(G, V)$ be a multiplicity free finite dimensional representation of a connected reductive complex Lie group $G$ and $G'$ be its derived subgroup. Assume that the categorical quotient $V//G$ is one dimensional, i.e., there exists a polynomial $f$ generating the algebra of $G'$-invariant polynomials on $V ({\mathbb C} [V]^{G'} = {\mathbb C} [f])$ and such that $f \not\in \mathbb C[V]^G )$. We prove that the category of regular holonomic $D_V$-modules invariant under the action of $G$ is equivalent to the category of graded modules of finite type over a suitable algebra.